Lyapunov-like characterizations for the concepts of nonuniform in time robust global asymptotic stability and input-to-state stability for time-varying systems are established. The main result of our work enables us to derive (1) necessary and sufficient conditions for feedback stabilization for affine in the control systems and (2) sufficient conditions for the propagation of the input-to-stat...

In this paper we provide a rather complete set of passivity suuciency conditions that give asymptotic stabilizability of nonlinear cascades of driving-driven systems. Moreover, we analyze the input-output and input-to-state stability properties of existing stabilization schemes. This allows us to derive the weakest passivity assumption on the driving system that give the required stability. In ...

In this work we discuss nonuniform and semi-uniform input-to-state stability (iss) properties for time-varying systems. Treating the iss properties for a time varying system as properties related to output stability for a time invariant auxiliary system, we provide several characterizations in terms of Lyapunov functions and the asymptotic gains; as well as a small gain theorem, for the time va...

This paper is devoted to stability analysis and synthesis of uncertain systems subject to input saturation. A new parameter-dependent Lyapunov function analyzing approach is proposed to reduce the conservatism in stability analysis for the polytopic systems subject to input saturation. Some new stability conditions and a gain-scheduling controller design method are then developed by the LMI opt...

Reliable stabilizing controller design with integral-action is considered for linear time-invariant, multi-input–multi-output decentralized systems with stable plants. Design methods are proposed to achieve reliable closed-loop stability with integral-action in each output channel for asymptotic tracking of step-input references applied at each input. The design approaches guarantee stability a...

The paper comprises a study of absolute stability, input-to-state stability, and boundedness properties of a feedback interconnection of a finite-dimensional, linear, m-input, m-output system (A, B, C) and a set-valued nonlinearity Φ. With reference to Figure 1, we assume that D is a set-valued map in which input or disturbance signals are embedded. The analytical framework is of sufficient gen...

This paper develops a unified framework for studying robustness of the input-to-state stability (ISS) property and presents new results on robustness of ISS to slowly varying parameters, to rapidly varying signals, and to generalized singular perturbations.

We consider the system

The problems of design and analysis of the nonlinear control systems are at the center of attention of the scientific community for several decades, but it was only during the last two decades that an appreciable progress was marked in the design and application of various methods of the theory of nonlinear control. On the one hand, this success is due to the development of the computer enginee...

For nonlinear input systems of general form, we prove that bounded-input bounded-state stability is equivalent to the existence of a time-dependent Liapunov function which is not necessarily continuous.